Considering we are basically pattern recognising machines it's fairly easy to spot alternate accounts. Although, a normal user may not have the proof which you ask for I'm almost certain Badbear would, however that doesn't mean he can give that information away either to an individual or publicly. Anyway, why would Badbear lie about having information? It wouldn't benefit him in anyway, it could only damage is reputation if found out.
I can guarantee you BadBear didn't base his feedback just off another member's, and it doesn't have to be just down to the same IP. If they both use exactly the same browser and operating system then that's good enough evidence in this case (and he may have other evidence I'm not aware of). Also, you're right that people sticking up for another isn't conclusive evidence alone but it certainly arouses suspicion, especially when they type the same way and use the same insults etc. More than a coincidence is it not?
To be fair if they are all using Windows then it doesn't really help the case, or even ubuntu. If they are using another operating system then it could be more obvious. Same goes as the browser. Most users probably vary with both operating system and browser, I know I've logged in on about 5 different operating systems and browsers because some browsers aren't easy to setup in some distributions. But, you are right if they all match then it does raise suspicious that much more.